Please read everything before to assume things

I don't mind that my girlfriend goes dancing alone or with friends, I trust her. It's something that I do too and I would never, ever dream of making a fuss about such a thing. The problem is that she says she wants to dance with the guys she meets at the club, and I honestly find that absurd. If I go to dance with a girl in the club I go to "flirt" with her it's not for the fun of dancing, if I just want to dance I stay with my friends. Let me be clear it is not a problem for me if you want to dance with a guy dances like Salsa or Tango but in the disco everything is designed to seduce the other person (and I feel I have to say that I speak as an Italian in Italy so it doesn't surprises me if those who are from non-latin countries do not follow my point) but stuff as "petting" or "touching" , even on the dance floor, the other person is quite on the agenda.

I told her about the fact that I'm not a big fan of it, she answered that for her there's nothing wrong if you don't go all the way with it and I told her in all honesty that if she will do it I would break up with her.

It doesn't want to be a threat and I know it sounds like one. But I see it as a lacking of respect of my feelings, I don't know if I can change this view.

For me it's the same as texting on tinder, yeah maybe you don't go out with them, yeah it's just for fun but still. I really like this girl there's a connection, I don't want to lose her but still I am not interested in a relationship where I'm hurt.

I don't know what to think